On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. II
type: Item
instance of: scholarly article
title: On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. II
zbMATH Open document ID: 1020.47029
author: V. A. Liskevich
author: Zeev Sobol
author: Hendrik Vogt
published in: Journal of Functional Analysis
publication date: 2002-11-28T00:00:00Z
review text: [For Part I, see the preceding review)]. The authors continue to study the \(L_p\) properties of second-order elliptic differential operators corresponding to expressions \(\Lambda=-\nabla.(a\nabla) + b.\nabla+ \nabla.c+V\) with singular measurable coefficients \(a,b,c,V\). Here, they consider the case of uniformly elliptic operators. They obtain the interval \((p_{\min}, p_{\max})\) in the \(L_p\)-scale, where the associated quasi-contractive \(C_0\)-semigroups can be defined on \(L_p\) spaces. The Sharpness of the main result is proven and the analyticity of the generators are given for \(p\) where the semigroup is defined.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D09
zbMATH DE Number: 1836672
zbMATH Keywords: \(L_p\) properties of second-order elliptic differential operators
zbMATH Keywords: quasi-contractive \(C_0\)-semigroups
zbMATH Keywords: uniformly elliptic operators
reviewed by: Miklavž Mastinšek
MaRDI profile type: Publication
full work available at URL: jfan.2001.3909
OpenAlex ID: W4213213085
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DOI: 10.1006/JFAN.2001.3909
description: scientific article; zbMATH DE number 1836672